Typists were taught to do it generally, but the origin of the
practice is to assist the typesetters.
No so. It predates typewriters and one can see this style in the typography in many books of the Victorian era and the early decades of the twentieth century.
From Robert Bringhurst's _Typographic Manual of Style_, pp. 28-30:
<< In the nineteenth century, which was a dark and inflationary age in typography and type design, many compositors were encouraged to stuff extra space between sentences. Generation of twentieth-centry typists were then taught to do the same, by hitting the spacebar twice after every period. Your typing as well as your typesetting will benefit from unlearning this quaint Victorian habit. As a general rule, no more than a single space is required after a period , a colon or any other mark of puctuation. Larger spaces (e.g., en spaces) are *themselves* punctuation.
The rule is usually altered, however, when setting classical Latin and Greek, romanized Sanskrit, phonetics or other kinds of texts in which sentences begin with lowercase letters. In the absence of a capital, a full en space (M/2) between sentences will generally be welcome. >>
For discussion of when double spacing after a period might still be good practice see http://desktoppub.about.com/library/weekly/blrules-spaces.htm and http://www.evolt.org/article/Two_Spaces_After_a_Period_Isn_t_Dead_Yet/25/213/?format=print.
Jim Allan